AC9M4N07 • Homework

Estimation, Rounding and Reasonableness worksheet

Use this printable homework sheet for written working, application and reflection alongside the online learning activities.

Open practice

Written practice: draw, explain and check

These eight tasks cover the whole topic. Show your working or model before checking the answers. The PDF includes writing space and an answer guide.

  1. Round 3 486 to the nearest ten and hundred. Then estimate 3 486 + 1 518 by rounding both addends to the nearest hundred. Calculate exactly and compare.

  2. Six packets cost $3.65 each. Use $3 and $4 per packet to find lower and upper bounds for the total. Explain why the actual cost is between them.

  3. A shopping list has prices $7.20, $12.10, $5.85 and $3.05. Round each upward to a whole dollar and total an estimated budget. Explain what this estimate guarantees for these items alone.

  4. The exact sum 458 + 342 is 800. Compare both-down hundreds rounding, both-up rounding and the mixed estimate 500 + 300. Which is closest, and why?

  5. The exact product 12 × 31 is 372. Compare both-down 10 × 30, mixed 20 × 30 and both-up 20 × 40. Which estimate is closest? What does this show about mixed rounding?

  6. You pay $40 for items costing $12.65 and $9.20. Round each price to the nearest dollar to estimate the change. Then find the exact change and explain why the estimate alone cannot confirm the cents.

  7. Use the compatible calculation 540 ÷ 9 to estimate 547 ÷ 9. Explain whether a displayed answer of 610 has a reasonable size.

  8. A shopper has $25 for items costing $8.10, $7.20 and $8.30. An upward whole-dollar estimate is $26. Does that prove the shopper lacks enough money? Calculate exactly and explain.

Answer guide for parents and teachers
  1. 3 486 rounds to 3 490 and 3 500. The hundreds estimate is 3 500 + 1 500 = 5 000. The exact sum is 5 004, only 4 above the estimate, so its size is reasonable.
  2. Six packets cost more than 6 × $3 = $18 and less than 6 × $4 = $24. Each actual price is between the two price bounds. The exact total is $21.90, which is inside the interval.
  3. The upward prices are $8, $13, $6 and $4, totalling $31. Each is at least its actual price, so $31 covers the listed items. The exact total is $28.20; the upper estimate need not be the exact bill.
  4. Both down: 400 + 300 = 700, 100 low. Both up: 500 + 400 = 900, 100 high. Mixed: 500 + 300 = 800, exactly correct here because the +42 and −42 changes cancel.
  5. The estimates are 300, 600 and 800, with errors 72, 228 and 428. Both-down 300 is closest in this case. Mixed rounding is not always closest; compare the actual errors.
  6. Estimated cost: $13 + $9 = $22, so change is about $18. Exact cost: $21.85, giving $18.15 change. Estimation checks size but does not verify every cent.
  7. 540 ÷ 9 = 60, so 547 ÷ 9 is a little more than 60. An answer of 610 is far too large. This is an estimate; no exact decimal quotient is needed.
  8. No. An upper estimate can exceed the budget while the actual bill is lower. The exact total is $23.60, so $25 is enough, leaving $1.40. The $26 estimate alone did not settle the decision.